Integral-form conjecture for Jack superpolynomials

Let ${\Lambda}$ and $\Om$ be superpartitions with $\Om\leq {\Lambda}$ in dominance order. Define the integral-form Jack superpolynomial by $J_{\Lambda}^{(\alpha)}=v_{\Lambda}(\alpha)P_{\Lambda}^{(\alpha)}$ and expand it as

$$J_{\Lambda}^{(\alpha)}=\sum_{\Om\leq{\Lambda}}v_{{\Lambda}\Om}(\alpha)m_{\Om}.$$

Integral-form conjecture. The coefficients $v_{{\Lambda}\Om}(\alpha)$ are polynomials in $\alpha$ with integer coefficients, so that $v_{{\Lambda}\Om}(\alpha)\in\mathbb Z[\alpha]$. This conjecture concerns the expected integrality of the Jack superpolynomial normalization; the source presents it as an open problem.